CAT 2025 Formula Sheet PDF: All Important Quantitative Aptitude Formulas for Quick Revision

Key Features of the CAT 2025 Formula Sheet

The CAT 2025 Formula Sheet is a strategic resource designed to help aspirants quickly revise and recall essential formulas across key topics like Arithmetic, Algebra, Geometry, and Trigonometry. It enhances exam preparation by offering structured, topic-wise Quantitative Aptitude formulas that improve problem-solving efficiency and accuracy during the CAT exam. This sheet consists of important formulas that candidates require during CAT preparation, ensuring students have everything they need in one place.

1. Topic-Wise Segregation for Focused Preparation

The CAT 2025 Formula Sheet is systematically divided into core Quantitative Aptitude topics such as Arithmetic, Algebra, Geometry, Trigonometry, and Number System. This organised structure helps aspirants target specific areas during revision. The clear division of important formulas for CAT preparation makes it easier to build accuracy step by step.

2. Comprehensive and Exam-Relevant Formulas

It includes all important formulas for CAT quant that are frequently tested in past exams. Only high-utility formulas that directly aid in solving Quant questions are included. By providing a selective formulas list for the CAT exam, it helps students avoid distractions and concentrate on formulas with the highest exam relevance and scoring potential.

3. High-Visibility Layout for Quick Recall

Designed with readability in mind, the sheet uses bold headings, colour-coded sections, and concise formats to make it visually appealing and easy to scan. Since important formulas for CAT preparation need to be revised multiple times, this format makes it highly effective for complete CAT 2025 revision, especially when quick recall is essential.

4. Quick Revision-Friendly Format

Ideal for daily practice and mock test preparation, the formula sheet allows aspirants to revise all crucial formulas quickly. It is also useful for learning shortcuts and tricks for CAT quant that save time in the exam. For serious aspirants, having the important formulas for CAT preparation ready helps in mastering speed-based problem-solving techniques required for the Quantitative Aptitude section.

5. Updated According to the Latest CAT Exam Pattern

The formula sheet is regularly updated based on the latest trends, question formats, and difficulty levels observed in recent CAT exams. This ensures that aspirants are not only revising the right formulas but also staying aligned with the current CAT exam syllabus. By consistently practising the must-know formulas for CAT 2025, students can boost confidence and accuracy.

CAT Important Formulas of Geometry

Mastering important geometry formulas is crucial for cracking the CAT exam, as geometry is a key topic in the Quantitative Aptitude section. The following section covers all essential CAT geometry formulas, including areas, polygons, angles, and properties of triangles and circles to help you solve problems quickly and accurately.

CAT Important Formulas of Trigonometry

Trigonometry plays a vital role in the CAT Quantitative Aptitude section, making it essential to learn and memorise key formulas. This comprehensive list of important CAT trigonometry formulas helps aspirants solve complex problems with speed, accuracy, and confidence during the exam.

1. Basic Trigonometric Ratios

These are defined in relation to a right-angled triangle:

• sin⁡θ=Opposite sideHypotenuse

• cos⁡θ=Adjacent sideHypotenuse

• tan⁡θ=Opposite sideAdjacent side

• csc⁡θ=HypotenuseOpposite side

• sec⁡θ=HypotenuseAdjacent side

• cot⁡θ=Adjacent sideOpposite side

2. Pythagorean Identities

• sin2⁡θ+cos2⁡θ=1

• 1+tan2⁡θ=sec2⁡θ

• 1+cot2⁡θ=csc2⁡θ

3. Trigonometric Functions of Negative Angles

• sin⁡(−θ)=−sin⁡θ

• cos⁡(−θ)=cos⁡θ

• tan⁡(−θ)=−tan⁡θ

• csc⁡(−θ)=−csc⁡θ

• sec⁡(−θ)=sec⁡θ

• cot⁡(−θ)=−cot⁡θ

4. Angle Sum and Difference Formulas

• sin⁡(A+B)=sin⁡Acos⁡B+cos⁡Asin⁡B

• sin⁡(A−B)=sin⁡Acos⁡B−cos⁡Asin⁡B

• cos⁡(A+B)=cos⁡Acos⁡B−sin⁡Asin⁡B

• cos⁡(A−B)=cos⁡Acos⁡B+sin⁡Asin⁡B

• tan⁡(A+B)=tan⁡A+tan⁡B1−tan⁡Atan⁡B

• tan⁡(A−B)=tan⁡A−tan⁡B1+tan⁡Atan⁡B

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Quantitative Aptitude Formulae for CAT 2025

Quantitative Aptitude formulas form the foundation of the Quantitative Aptitude section in the CAT 2025 exam. Here are some important CAT 2025 quant section-wise formulae for CAT 2025 preparation:

Arithmetic

The Arithmetic section is the most important section in the Quantitative Aptitude Section, which is also useful to solve the Data Interpretation problems. Following are some 50+ Important Formulas for CAT Preparation of this section which are given in this CAT Formula Sheet:

Percentage

Following are some Important CAT Formulas of percentage:

• X is what percentage of Y=XY×100

• X is what percentage more/less than Y=|X−Y|Y×100

Shortcut Formulas

Following are some formulas which can be used as CAT Quant Formulae:

Profit & Loss:

Following are some Important CAT Formulas of this topic:

Shortcut Formulas

Cheat Sheet for the preparation and exam point of view:

Simple Interest (S.I.) & Compound Interest (C.I.):

Following are some basic and Important Formulas for CAT 2025 related to Simple Interest and Compound Interest:

Shortcut Formulas

Following are some formulas which can be used as CAT Quant Formula Cheat Sheet for the preparation and exam point of view:

Time, Speed & Distance:

Following are some basic and Important Formulas for CAT 2025 related to Time, Speed and Distance:

Trains:

Boat & Streams:

Clocks

Shortcut Formulas

Following are some Quantitative Aptitude Formulas which can be used as a CAT Quant Formula Cheat Sheet for the preparation and exam point of view:

If the distance covered in each stage of the journey is the same, but speeds are different, then the average speed is the harmonic mean of the different speeds.
Ex: If distance between point A to B and B to C are same and are covered with the speed of s1 and s2 respectively. Then-
Average Speed = 2s1s2s1+s2

If the time taken in each stage of journey is same, but speeds are different, then the average speed is the average of the different speeds.
Ex: If time taken between points A to B and B to C is same and these distances are covered with the speed of s1 and s2 respectively. Then-
Average Speed = s1+s22

If two people start running on a circular track of length D km in the same direction from the same point with speeds a & b kmph, then-
(i) Time taken in first meeting = D|a−b| hr
(ii) Time taken to meet again at the starting point = LCM(Da,Db)
(iii) Number of distinct meeting points = |x−y|
{x & y are the simplified ratio of speeds, e.g. If speeds a & b are 12 kmph & 9 kmph respectively, then- x:y=12:9=4:3; So, x=4 & y=3}

If two people start running on a circular track of length D km in the opposite direction from the same point with speeds a & b kmph, then-
(i) Time taken in first meeting = Da+b hr
(ii) Time taken to meet again at the starting point = LCM(Da,Db) hr
(iii) Number of distinct meeting points = |x+y|
{x & y are the simplified ratio of speeds}

If a person P starts from A and heads towards B and another person Q starts from B and heads towards A and they meet after a time t then,
t=x⋅y
[where x = time taken (after meeting) by P to reach B and y = time taken (after meeting) by Q to reach A]

If the speed of the boat downstream is u kmph and the speed of the boat upstream is v kmph, then-
Speed of the boat in still water = u+v2 kmph
Rate of stream = u−v2 kmph

Geometry

The Geometry section is the lengthiest section in the Quantitative Aptitude Section which has lots of properties and formulas. Following are 50+ Important Formulas for CAT Preparation of this section which are given in this CAT Formula Sheet:

1. Triangles:

Properties of Triangles:

• The sum of all interior angles in a triangle is 180∘ and the sum of all exterior angles is 360∘.

• The sum of any two sides is always greater than the third one and the difference of any two sides is less than the third one.
  Let a,b,c be the sides of a triangle, then
  |b−c|<a<b+c

• In a scalene triangle the greatest side is always greater than one-third of the perimeter and less than half of the perimeter.
  Let a,b,c be the sides of the triangle and a be the greatest side. Let the perimeter be P. Then
  P3<a<P2

• Example: In a scalene triangle ABC, the perimeter is 24 cm and all sides are integers.
  Let a,b,c be sides of the triangle with a the greatest side. Then
  243<a<242
  8<a<12
  So possible values are 9,10,11 cm.

• For a,b,c sides of a triangle and a the greatest side:

  • If a2<b2+c2, then the triangle is acute angled.

  • If a2=b2+c2, then the triangle is right angled (Pythagoras theorem).

  • If a2>b2+c2, then the triangle is obtuse angled.

• (Here D is the midpoint of side AC, so AD=DC)

Midpoint of triangle

• Length of the Median –
  BD=122(AB2+BC2)−AC2

• 3× (Sum of squares of sides) =4× (Sum of squares of medians), that is,
  3(a2+b2+c2)=4(Ma2+Mb2+Mc2)
  where a,b,c are the sides of the triangle and Ma,Mb,Mc are the medians.

• In a right-angled triangle, Median of Hypotenuse =Hypotenuse2
  That is,
  CD=AB2

Median of hypotenuse

If all the medians are drawn in the triangle, then the 6 small triangles are generated in the triangle, which are equal in the Area.

Area of Triangle:

Heron’s Formula

If all sides of a triangle are given. Let a,b,c be the sides of the triangle –
Area = s(s−a)(s−b)(s−c) where s=a+b+c2 is the semiperimeter.

If two sides and the included angle are given –
Area = 12×Product of given sides×sin⁡(given included angle)
Area = 12×a×b×sin⁡C
(Example: sides a,b and included angle C are given)

If a side and its respective altitude (perpendicular drawn from the opposite vertex) is given, then –
Area of the triangle = 12×Base×Height (Altitude)

Shortcut Formulas

Area of an equilateral triangle = 34a2

Height (Altitude) of an equilateral triangle = 32a

Area of a triangle = r×s (where r is the inradius and s is the semiperimeter)

Area of a triangle = abc4R (where a,b,c are sides and R is the circumradius)

Quadrilaterals:

3. Circle:

• Circumference of a circle = 2πr

• Area of a circle = πr2

Semi-circle

• Circumference of a semi-circle = πr

• Perimeter of a semi-circle = πr+2r

• Area of a semi-circle = πr22

Sector & Segment of circle

{OAXC is called the sector of the circle & AXC is called the segment}

Length of arc AXC=θ360×2πr (where r is the radius)

Area of sector OAXC=θ360×πr2

2× Area of sector =Length of arc×Radius

Area of segment AXC=Area of sector OAXC−Area of △OAC

A=θ360πr2−12r2sin⁡θ

Where:
θ is the angle subtended at the center (in degrees)
r is the radius of the circle

Common Tangent

PQ and RS are the direct common tangents of the circles, which are equal in length.

Length of direct common tangent (L):
L2=d2−(r1−r2)2

Where:
d = distance between centers of the circles,
r1,r2 = radii of the circles.

PQ and RS are the transverse common tangents of the circles, which are equal in length.

Length of transverse common tangent (L):

L2=d2−(r1+r2)2

Where:
L is the length of the transverse common tangent
d is the distance between the centers of the two circles
r1 and r2 are the radii of the two circles

Mensuration:

Algebra

The Algebra section is a critical part of the Quantitative Aptitude section in the CAT exam. Below are over 50 important formulas for CAT preparation in this section, which are provided in this comprehensive CAT Formula Sheet:

1. Quadratic Equations

General Quadratic equation will be in the form of ax2+bx+c=0

Values of ‘x’ which satisfies the equation are called roots of the equation. To find the roots the Shreedhara Acharya's Formula is used.

Roots of the equation:
x=−b±b2−4ac2a

Sum of the roots = −ba

Product of the roots = ca

Difference of the roots = D where D=b2−4ac

If D>0, then the roots are real and distinct.
i. If D is a perfect square, then roots are rational; e.g. x=1,6
ii. If D is not a perfect square, roots are irrational or conjugate surds; e.g. x=3−5,3+5

If D=0, then the roots are real and equal.

If D<0, then the roots are imaginary and distinct.

For y=ax2+bx+c, where a>0,

• Minimum value occurs at x=−b2a and is given by:
  y=−D4a (Minimum value)

For y=ax2+bx+c, where a<0,

• Maximum value occurs at x=−b2a and is given by:
  y=−D4a (Maximum value)

Where D=b2−4ac is the discriminant.

If the roots of the quadratic equation are a and b, then the quadratic equation is:
x2−Sx+P=0 where S=a+b and P=ab
That is,
x2−(a+b)x+ab=0

Progression & Series

Arithmetic Progression (A.P.)

If a is the first term and d is the common difference then the Arithmetic Progression (A.P.). can be written as-

• a, a+d, a+2d, a+3d, …

Let a= first term

d= common difference

Nth term of the A.P. –
Tn=a+(n−1)d
Here, n is the number of terms.

Sum of the n terms of the A.P. (Sn) = Average of all the terms × number of terms (n).

Average of the terms can be found out easily:

• If the number of terms is odd, then the middle term will be the average.
  Example: 2,5,8,11,14 are terms of the A.P., then the middle term 8 is the average.
  So, Sn=average×n=8×5=40.

• If the number of terms is even, then the average of the middle two terms will be the average of the A.P.

Formula for sum of n terms:

Sn=n2[2a+(n−1)d]

Shortcut Formulae

Sn=n2(a+l)(where a=first term, l=last term, n=number of terms)

n=l−ad+1(number of terms in A.P.)

Geometric Progression (G.P.)

If a is the first term and r is the common ratio then the Geometric Progression (G.P.) can be written as-

a,a.r,a.r2,a.r3,…

Nth term of the G.P. –

Tn=a⋅rn−1 where n is the number of terms

Sum of the first n terms:

• If |r|<1:
  Sn=a⋅1−rn1−r

• If r>1:
  Sn=a⋅rn−1r−1

Sum of infinite terms of the G.P. (if |r|<1):
S∞=a1−r

Where:
a = first term,
r = common ratio,
n = number of terms

• |r|<1 ensures the series converges.

Shortcut Formulas

If there are odd no. of terms in a G.P., then the product of all terms are equal to the nth power of the middle term.

e.g. 2,6,18,54,162 are the terms of a G.P.

Then the products of all the terms = 185

Harmonic Progression (H.P.)

If a,b,c are in A.P., then 1a,1b,1c are in Harmonic Progression (H.P.).

n-th term of the H.P.=1n-th term of the corresponding A.P.

Series

Sum of first n natural numbers:
1+2+3+⋯+n=n(n+1)2

Sum of squares of first n natural numbers:
12+22+32+⋯+n2=n(n+1)(2n+1)6

Sum of cubes of first n natural numbers:
13+23+33+⋯+n3=(n(n+1)2)2

Sum of first n natural odd numbers:
1+3+5+⋯+(2n−1)=n2

Sum of squares of first n even numbers:
22+42+62+⋯+(2n)2=2n(n+1)(2n+1)3

Sum of squares of first n odd numbers:
12+32+52+⋯+(2n−1)2=n(2n+1)(2n−1)3

Indices & Surds

Product Rule:
am⋅an=am+n

Quotient Rule:
aman=am−n

Power of a Power:
(am)n=amn

Power of a Product:
(ab)n=an⋅bn

Power of a Quotient:
(ab)n=anbn

Negative Exponent:
a−n=1an

Shortcut Formulae

∏n=1∞an=limn→∞∏k=1nak

Logarithmic Rules and Properties

• Definition of Logarithm:
  logb⁡a=x⟺bx=a

• Log of 1:
  logb⁡1=0(for any base b>0,b≠1)

• Log of the base itself:
  logb⁡b=1

• Log of a product:
  logb⁡(mn)=logb⁡m+logb⁡n

• Log of a quotient:
  logb⁡(mn)=logb⁡m−logb⁡n

• Log of a power:
  logb⁡(mn)=n⋅logb⁡m

• Change of base formula:
  logb⁡a=logk⁡alogk⁡b(commonly with base 10 or e)

• Base switch rule:
  loga⁡b=1logb⁡a

Why is the CAT 2025 Formulae Important?

CAT 2025 Formulae is crucial for MBA exam preparation as it compiles important formulas for CAT preparation and concepts, streamlining study efforts and enhancing exam readiness. This resource not only aids in quick recall but also fosters a deeper understanding of quantitative topics.

• A consolidated CAT math formulas PDF allows for focused study sessions. It also reduces the time spent searching for formulas across various resources. For aspirants, keeping a formula list for CAT exam in one place ensures efficiency in revision.

• Regular use of the CAT formula PDF helps in developing quick problem-solving techniques. This is essential for tackling the time constraints of the exam. By practising with shortcuts and tricks for CAT quant, candidates can improve both speed and accuracy.

• The formula sheet highlights the important formulas for CAT 2025, making last-minute revision easier. It ensures that students cover all must-know formulas for CAT 2025 without missing high-priority areas.

• Familiarity with formulas leads to fewer mistakes during the test. This boosts both confidence and accuracy. Understanding which important formulas for CAT preparation are most relevant helps aspirants attempt strategically and maximise their scores.

How to Memorise Formulas for CAT Effectively

Learning important formulas for CAT preparation requires more than memorisation; it needs a strategy that blends practice with smart revision. Grouping important formulas for CAT preparation by topics like Arithmetic, Algebra, Geometry, and Trigonometry makes recall systematic and avoids confusion during the exam.

• Maintaining a dedicated notebook of important formulas for CAT preparation helps in quick revisions and also works as a personalised formulas list for CAT exam. Writing each formula with an example ensures you understand both its structure and application.

• Visual resources play a key role in remembering important formulas for CAT preparation, especially in Geometry and Trigonometry. Linking concepts with diagrams or mnemonics makes retention effortless and aligns with shortcuts and tricks for CAT quant.

• Consistent revision of important formulas for CAT preparation is vital. Turning your notes into a cat math formulas pdf allows you to revise on the go and keeps all essential content in one place.

• Lastly, solving practice questions using important formulas for CAT preparation reinforces memory and accuracy. This habit builds confidence and ensures you master the must-know formulas for CAT 2025 well before the exam.

Commonly Forgotten CAT Formulas You Must Revise

Many aspirants struggle because they overlook important formulas for CAT preparation that appear frequently in the exam. Simple percentage and ratio formulas, though basic, remain part of important formulas for CAT preparation and are often forgotten under time pressure.

• Geometry concepts like areas of circles, triangles, and polygons are key important formulas for CAT preparation that must be revised repeatedly, as skipping them can cost valuable marks. Similarly, algebraic identities such as (a+b)2(a+b)^2(a+b)2 and (a−b)2(a-b)^2(a−b)2 fall under important formulas for CAT Quant and often slip from memory if not revised consistently.

• In Quant, trigonometric ratios and identities are also important formulas for CAT preparation that aspirants tend to ignore, even though they frequently appear in questions. Keeping these in a formulas list for CAT exam helps minimise errors.

• The Number System contains divisibility rules and LCM-HCF shortcuts, both part of important formulas for CAT preparation, that students overlook while focusing on advanced topics. Converting them into a quick CAT math formulas PDF ensures they are revised regularly.

CAT Formula Applications in Previous Year Questions

Understanding the real use of important formulas for CAT preparation in previous year questions helps aspirants apply concepts accurately under exam conditions. Many questions rely on simple, important formulas for cat quant from Arithmetic, like percentages, profit-loss, and ratio-proportion, which appear repeatedly across years.

Geometry problems in past CAT papers often test important formulas for CAT 2025 involving triangles, circles, and polygons. Practising these helps students quickly recall relevant formulas during the exam. Similarly, algebraic expressions and identities are part of important formulas for CAT preparation that regularly appear in Quant questions, reinforcing the need for consistent revision.

Trigonometry and mensuration questions also use important formulas for CAT preparation, where knowing shortcuts can save precious time. Maintaining a CAT math formulas PDF or a formulas list for CAT exam ensures aspirants can revise these efficiently before attempting mocks.

Even Data Interpretation sets occasionally require important formulas for CAT preparation, such as averages, percentages, and ratios, to solve tables and charts accurately. Analysing previous years’ patterns helps aspirants identify which must-know formulas for CAT 2025 carry the highest weight, enhancing preparation strategy.

CAT Formula Shortcuts vs Detailed Methods

Mastering important formulas for CAT preparation is not just about memorising them—it’s about knowing when to use shortcuts versus detailed methods. Shortcuts save time in questions that follow standard patterns, while detailed methods help in complex or non-standard problems.

For example, in Arithmetic, important formulas for CAT Quant such as percentage-change or profit-loss can be solved using shortcuts to get instant answers. But sometimes, applying the formulas list for CAT exam in a step-by-step manner ensures accuracy in tricky scenarios.

Geometry problems often offer the choice between using important formulas for CAT preparation directly or solving them through detailed angle/length calculations. Knowing the shortcut method from a CAT math formulas PDF speeds up your pace, while detailed solutions act as a safety net for accuracy.

Algebra and Trigonometry questions also require important formulas for CAT preparation. Shortcuts here can reduce solving time, but understanding the underlying concept ensures you don’t make careless mistakes. Combining shortcuts and tricks for CAT quant with standard methods optimises both speed and reliability.

Benefits of Keeping CAT 2025 Formula Sheet PDF

Keeping a CAT 2025 Formula Sheet PDF helps aspirants quickly revise key mathematical concepts, shortcuts, and important formulas for CAT preparation. It serves as a ready reference during preparation, saves time, and ensures nothing important is missed while solving quantitative and reasoning problems.

Quick access to all important formulas in one place

A CAT 2025 Formula Sheet brings all essential equations and shortcuts from Quantitative Aptitude and Data Interpretation together, allowing you to refer to them instantly without flipping through multiple books or notes. It complements a detailed formulas list for CAT exam and ensures you stay focused on high-utility concepts.

Saves revision time during last-minute preparation

With the exam approaching, time becomes critical. A ready-made CAT 2025 Formula Sheet cuts down on revision time by offering a focused list of important formulas for CAT preparation, helping you stay organised and stress-free. Aspirants can also pair this with a CAT math formulas PDF for quicker revisions.

Improves speed and accuracy in problem-solving

Frequent review of formulas boosts familiarity, which leads to quicker recall during the exam. This naturally improves your speed and reduces calculation errors in time-bound situations. Using shortcuts and tricks for CAT quant along with important formulas for CAT 2025 strengthens both accuracy and efficiency.

Reduces the risk of forgetting key concepts

Revisiting formulas regularly through a dedicated sheet helps reinforce memory. This ensures that vital concepts stay fresh, especially for topics you may not practise every day. Including must-know formulas for CAT 2025 in your revision ensures full coverage of scoring areas.

Helps identify formula-based shortcuts for tricky questions

Many CAT questions can be solved faster with the right shortcuts. A CAT 2025 Formula Sheet highlights these quicker methods, helping you attempt more questions efficiently within the limited time frame. Regularly reviewing the important formulas for CAT preparation ensures you know which techniques to apply during the test.